I've recently been looking at some options for set-top boxes so that I can stream internet video to my TV. As far as I can tell, Amazon and Google have had a dispute, so you can't watch YouTube from an Amazon Fire and you can't watch Amazon Prime from a Chromecast. There are other devices that do both (along with Netflix and BBC iPlayer), eg Apple TV.
With that in mind, how does it work for WAM sites, eg MostWAM.tv? Do you need an app to access those sites or can you use a web browser on the box?
Most "apps' for a service that has a website are just a web browser with a unique skin and that website hard-coded into it. Many of them do nothing more than request a special version of the site arranged in a specific way. (i.e. the "mobile" version)
Any set-top box, USB stick, or media player device that includes a web browser should be able to display at least the regular computer-specific version of any site.
Remember that any device without a hard-wired ethernet connection on it is going to be subject to the speed and reliability of your WiFi system to pull down material from the internet. If you live in a large condo or apartment structure with hundreds of other people nearby all sharing those same frequencies, it's possible that you will have problems streaming HD and 4k material reliably from around 5pm to 10pm when everyone comes home from work, fires up the microwave (same frequency and they all leak a little), check their email, and starts up a Netflix video.
I have a $29 ROKU box attached to my TV that can access thousands of internet tv channels around the world.....but as far as wam content goes, there is nothing you can get using Roku or Amazon Fire Stick. Sure...you can get Youtube, but Youtube will not allow Wam Producers to maintain a full channel on their system without deleting us. I have had 3 of my prior Youtube channels shut down and they recently shut down the Mostwam Yoiutube channel as well.
The best way do do what you want to do....is actually really really simple and only costs $6.....
i.e. any streaming service that you can play on your tablet or smartphone...such as Mostwam.TV or Wamflix.com - all you have to do is buy a Micro USB to HDMI adapter cable like this....
What inputs does your TV have? A couple of winters ago I bought a fairly basic 50" flat screen TV from Tesco that has both HDMI and VGA inputs. When I want to watch a movie (or a WAM video) on the big screen I just use a long cable to plug my laptop's VGA-out into the TV's VGA in (sound goes from an external USB sound card to my main hi-fi but a cable from headphone-out to line-in on the TV would work just as well), and then anything I can play on my laptop I can have on the big screen, from Hollywood DVDs to my WAM collection.
Long term I plan to install a media-PC to drive the screen and not rely on the laptop but I've not got round to building that PC yet.
What I have connected to my TV is a mini PC like this one: N42 Fanless MINI PC, 4GB/64GB Intel Pentium N4200 (2M Cache, up to 2.5GHz) HD Graphics 505, 1000M/LAN 2.4G/5.8G Dual Band WIFI BT 4.0, Support M.2 NGFF SSD up to 256GB, Fanless Mini Desktop https://www.amazon.co.uk/dp/B0749J27Y2/ref=cm_sw_r_cp_api_p3PSBbFHQ9RDT
I have a Chromecast, and I can stream mostwam.tv and YouTube (And Netflix, and just about any other non-Amazon-owned streaming site(curiously enough I can stream Amazon music to it)), but I found it tended to freeze on newer (probably 4k) clips, and there's not really a good way of viewing anything from my personal collection (I can either download it to the phone and stream it from the Google photos app, which has a tendency to overheat the phone and quit; or stream the desktop from my PC in the other room, which has a more shall we say "variable" video quality, and the potential to alert the whole house to what I'm watching if I've forgotten to turn the speakers off).
So I more recently obtained an Asus Chromebit and a small bluetooth keyboard/mouse combo. This has been the best option for the bedroom TV. I can do on it anything I could do in the Chrome browser on my PC. I can stream any site that offers streaming. I've loaded my personal collection onto my Google drive and I can now stream it to the tv.
The only very minor downside (if the Chromebit is your only streaming device and you're into home theater) is it evidently doesn't output 5.1 audio, but that's one reason I've kept the Blu Ray player and Fire stick; and let's face it, nobody's watching this stuff for the audio. AFAIK, nobody's ever mixed a WAM video in 5.1 (why would you when that's money you could spend on more mess).
The attached screenshot shows mostwam.tv on my phone. If I tap the "cast" icon (upper right hand corner of the video frame, second icon in) it brings up a list of compatible devices on the network (in my case, the Chromecast and the Blu Ray player) and I tap the one I want to use.